2024/11/05 by Kujur, Ashish, Reza, Md Ramiz
#46E22 #47A62 #47B35 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2411.02962
A well known result of Brown and Halmos shows that the Toeplitz operators induced by L∞(\mathbb T) symbols on the Hardy space of the unit disc \mathbb D are characterized by the operator identity T_zATz=A, where Tz, T_z are the Toeplitz operators induced by the function z and z on the unit circle \mathbb T respectively. In this paper we introduce and study a class of Toeplitz operators on the Dirichlet space D 0 induced by a symbol class \mathcal T(\mathcal D 0)= H∞0(\mathbb D) + \mathcal M(\mathcal D0 ), where H∞0(\mathbb D) denotes the set of all bounded analytic function on \mathbb D vanishing at 0 and \mathcal M(\mathcal D 0) denotes the multiplier algebra of the Dirichlet space \mathcal D0. We find that the Toeplitz operators on the Dirichlet space \mathcal D induced by the symbol class \mathcal T(\mathcal D 0) is completely characterized by the operator identity T_zATz=A.